1. Field of the Invention
This invention relates to a strain wave gearing. More particularly, this invention relates to the tooth profiles of a rigid internal gear and a flexible external gear used in a strain wave gearing.
2. Background Art
A strain wave gearing typically consists of a rigid circular internal gear, a flexible external gear which has 2n fewer teeth than the internal gear and which is disposed inside the internal gear and flexed into an elliptical shape so as to mesh with the internal gear at, for example, two places, and a wave generator fitted inside the external gear for flexing it into an elliptical shape.
Although the tooth profiles of the gears of early strain wave gearings were linear (see U.S. Pat. No. 2,906,143), the present inventor demonstrated the possibility of using involute gears (see JP-B 45-41171). In addition, for increasing load capacity, the inventor proposed a system using as the tooth face profiles of both gears the curve obtained by similarity transforming the movement locus, at a reduction ratio of 1/2, over a prescribed range from the meshing limit point on the locus based on the rack approximation of the tooth of the external gear relative to the internal gear (JP-A 63-115943). This is a system for obtaining continuous contact between the tooth profiles of the tooth faces of both gears.
Based on studies of the three-dimensional phenomenon called coning in which the insertion of the elliptical wave generator causes the amount of deflection (half the difference between the major and minor axes of the ellipse) to gradually increase from the diaphragm side toward the end of a cup-shaped or silk-hat-shaped flexible external gear approximately in proportion to the distance from the diaphragm, the inventor developed strain wave gearings enabling a wide mesh range, without interference, over the entire tooth trace of the cup-shaped flexible external gear. These devices are described, for example, in JPA 5-172195, JPA 5-172196 and JPA 5-209655.
Other improved tooth profiles are proposed in, for example, JP-A 62-75153, JP-A 2-62461 and JP-A 7-167228. Among these, JP-A 7-167228 is of particular interest in that it utilizes tooth inclination to eliminate tooth profile interference.
The performance being demanded of strain wave gearings is becoming increasingly sophisticated. To respond to this demand, it is necessary to further improve device strength, rigidity and wear resistance.
Further consideration must be given to the tooth profile to achieve these improvements. The basic tooth profiles derived from the movement locus obtained by rack approximation must also be considered in light of the fact that some degree of tooth inclination and change in tooth movement locus arise in the case of finite teeth. The invention set out in the aforesaid JP-A 7-167228 ('228) is an improvement that focuses on tooth inclination to eliminate tooth interference.
However, the '228 invention does not sufficiently analyze tooth inclination and, moreover, gives no consideration to change in tooth movement locus. Thus while the '228 invention succeeds in avoiding tooth interference, it fails to maintain the feature to which the basic tooth profiles are directed, namely, the ability to achieve a wide mesh range. The reasons for this are that while it defines the tooth center line of the flexible external gear as the normal of the neutral curve (located substantially at the center of the tooth bottom rim of the flexible external gear and not contracted or expanded by deflection) and takes the angle between this normal and the radial line into account, it does not take into account the angle between this normal and the tooth space center line (the true tooth inclination angle), and further that it does not take in to account the fact that the movement locus of the intersection point between the tooth center line and the neutral curve, i.e., the origin of the coordinate system for motion analysis, differs from that in the case of a rack.
The object of this invention is to provide a strain wave gearing having non-interfering wide mesh range tooth profile wherein tooth inclination and change in the movemen locus of the origin of the tooth profile coordinate system are taken into account with respect to a rack-approximated tooth profile, thereby enabling correct meshing over a wide range.